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<h1 class="reftitle">block</h1>
<h2>Purpose</h2>
<p>Adds a move blocking constraint</p>
<h2>Syntax</h2>
<pre class="synopsis"></pre>
<h2>Description</h2>
<p></p> 
    Adding this filter to an MPC setup will modify the constraints in
    such a way that the differences between several consecutive
    optimization variables are equal to zero.<br><br>

    In the most common scenario, adding this filter to a signal
    representing control inputs will add a move-blocking constraint,
    which is equivalent to setting a control horizon.<br><br>

    To enable this filter, call <tt>model.u.with('block')</tt> (note
    that you can add this constrain to any type of signals, e.g., to
    state and output signals as well).<br><br>

    Once the filter is enabled, parameters of the blocking scheme can
    be specified in the <tt>model.u.block.from</tt> and
    <tt>model.u.block.to</tt> parameters. Setting these values to
    non-zero integers will add the constraint <img src="../../../../../fig/mpt/modules/ui/@SystemSignal/filter_block1.png" alt="../../../../../fig/mpt/modules/ui/@SystemSignal/filter_block1.png">.<br><br>

    The filter can be removed by calling
    <tt>model.x.without('block')</tt>. 

  <h2>Example(s)</h2>
<h3>Example 
				1</h3>Create a 1D LTI system <img src="../../../../../fig/mpt/modules/ui/@SystemSignal/filter_block2.png" alt="../../../../../fig/mpt/modules/ui/@SystemSignal/filter_block2.png">.<pre class="programlisting">model = LTISystem('A', 0.9, 'B', 1);</pre>
<pre class="programlisting"></pre>Add constraints and penalties<pre class="programlisting">
		model.x.min = -4; model.x.max = 4;
		model.u.min = -1; model.u.max = 1;
		model.x.penalty = QuadFunction(1);
		model.u.penalty = QuadFunction(1);
	</pre>
<pre class="programlisting"></pre>Create an MPC controller with prediction horizon 10<pre class="programlisting">M = MPCController(model, 5);</pre>
<pre class="programlisting"></pre>Tell the controller that only the first two control moves
    are free, the rest are to fixed<pre class="programlisting">
		M.model.u.with('block');
		M.model.u.block.from = 2;
		M.model.u.block.to = 5;
		x0 = 4;
		[~, ~, openloop] = M.evaluate(x0);
		openloop.U
	</pre>
<pre class="programlisting">
ans =

                        -1        -0.719434753448955        -0.719434753448955        -0.719434753448955        -0.719434753448955

</pre>
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<br><p>©  <b>2003-2013</b>     Michal Kvasnica: STU Bratislava,    <a href="mailto:michal.kvasnica@stuba.sk">michal.kvasnica@stuba.sk</a></p>
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